Results 1 to 10 of about 232 (187)
Barekeng, 2023 Let be a bounded open subset of , , be a function in Stummel classes , where , and be a semilinear monotone elliptic equation, where is symmetric matrix, elliptic, bounded, and is non decreasing and Lipschitz. By proving a weighted estimation for
Nicky Kurnia Tumalun
doaj +1 more source
Topological Derivatives for Semilinear Elliptic Equations [PDF]
International Journal of Applied Mathematics and Computer Science, 2009 Topological Derivatives for Semilinear Elliptic EquationsThe form of topological derivatives for an integral shape functional is derived for a class of semilinear elliptic equations. The convergence of finite element approximation for the topological derivatives is shown and the error estimates in theL∞norm are obtained.
Mohamed Iguernane +4 more
openaire +3 more sources
Nondegeneracy of the bubble solutions for critical equations involving the polyharmonic operator
Boundary Value Problems, 2023 We reprove a result by Bartsch, Weth, and Willem (Calc. Var. Partial Differ. Equ. 18(3):253–268, 2003) concerning the nondegeneracy of bubble solutions for a critical semilinear elliptic equation involving the polyharmonic operator.
Dandan Yang +3 more
doaj +1 more source
On a Model Semilinear Elliptic Equation in the Plane [PDF]
Journal of Mathematical Sciences, 2016 This paper deals with the blow-up problem for a model semilinear equation of the type \[ \text{div}(A(z)\nabla u)= e^u \] in a simply connected domain \(\Omega\subset \mathbb{C}^1\). \(A(z)\) is a \(2\times 2\) symmetric uniformly elliptic matrix with measurable entries and \(\text{det\,}A=1\).
Gutlyanskii, V.Y. +2 more
openaire +3 more sources
Solutions of Semilinear Elliptic Equations in Tubes [PDF]
Journal of Geometric Analysis, 2012 Given a smooth compact k-dimensional manifold Λembedded in $\mathbb {R}^m$, with m\geq 2 and 1\leq k\leq m-1, and given ε>0, we define B_ε(Λ) to be the geodesic tubular neighborhood of radius εabout Λ. In this paper, we construct positive solutions of the semilinear elliptic equation Δu + u^p = 0 in B_ε(Λ) with u = 0 on \partial B_ε(Λ), when the ...
Frank Pacard +2 more
openaire +3 more sources
Multiple solutions for a semilinear elliptic equation [PDF]
Transactions of the American Mathematical Society, 1995 Let Ω \Omega be a bounded, smooth ...
del Pino, Manuel A., Felmer, Patricio L.
openaire +2 more sources
A Concentration Phenomenon for Semilinear Elliptic Equations [PDF]
Archive for Rational Mechanics and Analysis, 2012 For a domain $Ω\subset\dR^N$ we consider the equation $ -Δu + V(x)u = Q_n(x)\abs{u}^{p-2}u$ with zero Dirichlet boundary conditions and $p\in(2,2^*)$. Here $V\ge 0$ and $Q_n$ are bounded functions that are positive in a region contained in $Ω$ and negative outside, and such that the sets $\{Q_n>0\}$ shrink to a point $x_0\inΩ$ as $n\to\infty$.
Ackermann, Nils, Szulkin, Andrzej
openaire +2 more sources
Quasi-concavity for semilinear elliptic equations with non-monotone and anisotropic nonlinearities
Boundary Value Problems, 2006 A boundary-value problem for a semilinear elliptic equation in a convex ring is considered. Under suitable structural conditions, any classical solution u lying between its (constant) boundary values is shown to decrease along each ray starting from the ...
Antonio Greco
doaj +4 more sources
The structure of solutions of a semilinear elliptic equation [PDF]
Transactions of the American Mathematical Society, 1992 We give a complete classification of solutions of the elliptic equation Δ u
Cheng, Kuo-Shung, Lin, Tai-Chia
openaire +2 more sources
Isolated boundary singularities of semilinear elliptic equations [PDF]
Calculus of Variations and Partial Differential Equations, 2010 Given a smooth domain $Ω\subset\RR^N$ such that $0 \in \partialΩ$ and given a nonnegative smooth function $ζ$ on $\partialΩ$, we study the behavior near 0 of positive solutions of $-Δu=u^q$ in $Ω$ such that $u = ζ$ on $\partialΩ\setminus\{0\}$. We prove that if $\frac{N+1}{N-1} < q < \frac{N+2}{N-2}$, then $u(x)\leq C \abs{x}^{-\frac{2}{q-1 ...
Bidaut-Veron, Marie-Françoise +2 more
openaire +3 more sources